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Cooperative games with homogeneous groups of participants

Author

Listed:
  • L. Hernández-Lamoneda
  • Francisco Sánchez-Sánchez

Abstract

We consider a class of games, which we call “groups’ games”, in which players are partitioned into classes within which players may be considered indistinguishable. We compute explicit formulas for some of the principal values restricted to these games. This is particularly useful for dealing with games with a large number of players where the usual formulas would be impractical (or impossible) to compute. We give several examples that illustrate how this idea may be applied to concrete situations. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • L. Hernández-Lamoneda & Francisco Sánchez-Sánchez, 2015. "Cooperative games with homogeneous groups of participants," Theory and Decision, Springer, vol. 79(3), pages 451-461, November.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:3:p:451-461
    DOI: 10.1007/s11238-014-9474-8
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    References listed on IDEAS

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    1. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    2. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, September.
    3. L. Hernández-Lamoneda & R. Juárez & F. Sánchez-Sánchez, 2007. "Dissection of solutions in cooperative game theory using representation techniques," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(3), pages 395-426, February.
    4. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    5. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    6. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
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